This invention relates to phase matching in a laser light emitting apparatus that uses a lithium niobate (LiNbO.sub.3) crystal as a second harmonic generating crystal.
In performing second harmonic generation (SHG) using a Nd-YAG laser and a LiNbO.sub.3 crystal, non-critical phase matching (.theta.=90.degree.) is desired since the best physical properties are expected at that point. However, since it has been impossible to attain non-critical phase matching at room temperature, a temperature matching method has conventionally been employed in which a LiNbO.sub.3 crystal is heated. In this method, to obtain non-critical phase matching, the LiNbO.sub.3 crystal is placed in an oven and its temperature is adjusted to achieve uniform heating of the crystal.
With the LiNbO.sub.3 crystal, the walkoff angle .rho. is given by the following formula: ##EQU1## where n.sub..omega..sup.o : refractive index for fundamental (.omega.) ordinary light;
n.sub.2.omega..sup.o : refractive index for second harmonic (2.omega.) ordinary light; PA1 n.sub.2.omega..sup.e : refractive index for second harmonic (2.omega.) extraordinary light; and PA1 .theta..sub.m : phase matching angle. This formula shows that .rho. is approximately zero when .theta..sub.m =90.degree.. Hence, the effective SHG length corresponds to the crystal length.
The allowance angle .delta..theta. is given by the following equation: ##EQU2## where l: crystal length; and .lambda..sub..omega. : wavelength of a fundamental wave.
Substituting .DELTA.n=n.sub.2.omega..sup.o -n.sub.2.omega..sup.e =0.0998, l=10 mm and .lambda..sub.107 =1 .mu.m into this equation, we obtain .delta..theta.=22 mrad=1.26.degree.. Since the fundamental wave incident on the crystal with a beam divergence smaller than this value will take part in SHG, the fundamental wave can be focused by a lens so that it is effectively launched into the crystal.
If the phase matching angle .theta..sub.m is 80.degree., .rho. is approximately 0.36.degree. and .delta..theta. is 0.17.degree.. The value of .rho. is not significant in practical applications, but if .delta..theta. is small, high efficiency of SHG is not attained even if the incident light is focused by a lens.
Since phase matching at .theta.=90.degree. is possible by controlling the temperature of the LiNbO.sub.3 crystal, the current practice has been to heat the crystal in an oven. However, this causes the problem that a large oven is necessary to heat the entire crystal uniformly.
A KTP (Potassium Titanyl Phosphate) crystal is suitable for SHG using an LD-pumped Nd-YAG laser. However, KTP crystals are synthesized by a hydrothermal or flux crystal growth method, either of which takes about one month and is therefore costly.